Question

determine if lines q and v are parallel.
select the correct choice below and fill in the answer box(es) to complete your choice.
a. the slope of line q is , and the slope of line v is . since the product of their slopes is - 1, lines q and v are parallel. (simplify your answers.)
b. the slope of line q is , and the slope of line v is . since the slopes are different, lines q and v are not parallel. (simplify your answers.)
c. the slope of line q is , and the slope of line v is . since the product of their slopes is not - 1, lines q and v are not parallel. (simplify your answers.)
d. since both lines have a slope of , lines q and v are parallel. (simplify your answer.)

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Find slope of line q

Let's assume two points on line q, say $(x_1,y_1)$ and $(x_2,y_2)$. Count the rise (change in y - values) and run (change in x - values) between two distinct points on line q. Suppose the two points on line q are $(x_1,y_1)=( - 8,6)$ and $(x_2,y_2)=(2, - 4)$. Then $m_q=\frac{-4 - 6}{2+8}=\frac{-10}{10}=-1$.

Step3: Find slope of line v

Let's assume two points on line v, say $(x_3,y_3)$ and $(x_4,y_4)$. Suppose the two points on line v are $(x_3,y_3)=( - 6,2)$ and $(x_4,y_4)=(4, - 8)$. Then $m_v=\frac{-8 - 2}{4 + 6}=\frac{-10}{10}=-1$.

Step4: Determine parallelism

Since both lines have a slope of - 1, lines q and v are parallel.

Answer:

D. Since both lines have a slope of - 1, lines q and v are parallel.